Date | November Example question | Marks available | 4 | Reference code | EXN.1.SL.TZ0.12 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Find | Question number | 12 | Adapted from | N/A |
Question
A disc is divided into 9 sectors, number 1 to 9. The angles at the centre of each of the sectors un form an arithmetic sequence, with u1 being the largest angle.
It is given that u9=13u1.
Write down the value of 9Σi=1ui.
Find the value of u1.
A game is played in which the arrow attached to the centre of the disc is spun and the sector in which the arrow stops is noted. If the arrow stops in sector 1 the player wins 10 points, otherwise they lose 2 points.
Let X be the number of points won
Find E(X).
Markscheme
* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.
360° A1
[1 mark]
EITHER
360=92(u1+u9) M1
360=92(u1+13u1)=6u1 M1A1
OR
360=92(2u1+8d) M1
u9=13u1=u1+8d⇒u1=-12d M1
Substitute this value 360=92(2u1-8×u112) (=92×43u1=6u1) A1
THEN
u1=60° A1
[4 marks]
E(X)=10×60360-2×300360=0 M1A1
[2 marks]